Chapter 3.05: Implicit Differentiation
#1
#7
#27
#28 WEP
#57
#63
#71 WEP
#73 WEP
#74 WEP
#77 MTH/MTHT
#79a WEP

QA: WEP
i) Suppose I put two thumbtacks into a piece of paper at (-3cm,0) and (+3cm,0).
Then I take a string and tie it to each thumbtack, leaving a length of
8 cm of string from one thumbtack to the other. Then I use a pencil point
to pull the string taut and move it around, so the distance from one tack
to the pencil point to the other tack is always 8 cm. Write an implicit
equation that describes this situation, which we can rephrase as:
the sum of the distances from the pencil point to the two thumbtacks
is always 8 cm.

ii) What geometric figure do you get from that situation?

iii) Ignore the string analogy for now. What if the _difference_ of the
distances is always 2 cm, rather than the sum being 8 cm? What equation
do you get?

iv) What geometric figure do you get from that situation?


QB: WEP
Like #35-38, find y'' for x^2+y^2=r^2.
Graph it along with y' and the original function to make sure
your answer is reasonable.
You could also solve x^2+y^2=r^2 for y and find the 2nd
derivative that way, as another way to check it.